-void AliKalmanTrack::External2Helix(Double_t helix[6]) const {
- //--------------------------------------------------------------------
- // External track parameters -> helix parameters
- //--------------------------------------------------------------------
- Double_t alpha,x,cs,sn;
- GetExternalParameters(x,helix); alpha=GetAlpha();
-
- cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
- helix[5]=x*cs - helix[0]*sn; // x0
- helix[0]=x*sn + helix[0]*cs; // y0
-//helix[1]= // z0
- helix[2]=TMath::ASin(helix[2]) + alpha; // phi0
-//helix[3]= // tgl
- helix[4]=helix[4]/GetLocalConvConst(); // C
-}
-
-static void Evaluate(const Double_t *h, Double_t t,
- Double_t r[3], //radius vector
- Double_t g[3], //first defivatives
- Double_t gg[3]) //second derivatives
-{
- //--------------------------------------------------------------------
- // Calculate position of a point on a track and some derivatives
- //--------------------------------------------------------------------
- Double_t phase=h[4]*t+h[2];
- Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
-
- r[0] = h[5] + (sn - h[6])/h[4];
- r[1] = h[0] - (cs - h[7])/h[4];
- r[2] = h[1] + h[3]*t;
-
- g[0] = cs; g[1]=sn; g[2]=h[3];
-
- gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
-}
-
-Double_t AliKalmanTrack::
-GetDCA(const AliKalmanTrack *p, Double_t &xthis, Double_t &xp) const {
- //------------------------------------------------------------
- // Returns the (weighed !) distance of closest approach between
- // this track and the track passed as the argument.
- // Other returned values:
- // xthis, xt - coordinates of tracks' reference planes at the DCA
- //-----------------------------------------------------------
- Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
- Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
- Double_t dx2=dy2;
-
- //dx2=dy2=dz2=1.;
-
- Double_t p1[8]; External2Helix(p1);
- p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
- Double_t p2[8]; p->External2Helix(p2);
- p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
-
-
- Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
- Evaluate(p1,t1,r1,g1,gg1);
- Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
- Evaluate(p2,t2,r2,g2,gg2);
-
- Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
- Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
-
- Int_t max=27;
- while (max--) {
- Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
- Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
- Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
- (g1[1]*g1[1] - dy*gg1[1])/dy2 +
- (g1[2]*g1[2] - dz*gg1[2])/dz2;
- Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
- (g2[1]*g2[1] + dy*gg2[1])/dy2 +
- (g2[2]*g2[2] + dz*gg2[2])/dz2;
- Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
-
- Double_t det=h11*h22-h12*h12;
-
- Double_t dt1,dt2;
- if (TMath::Abs(det)<1.e-33) {
- //(quasi)singular Hessian
- dt1=-gt1; dt2=-gt2;
- } else {
- dt1=-(gt1*h22 - gt2*h12)/det;
- dt2=-(h11*gt2 - h12*gt1)/det;
- }
-
- if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
-
- //check delta(phase1) ?
- //check delta(phase2) ?
-
- if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
- if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
- if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
- AliWarning(" stopped at not a stationary point !");
- Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
- if (lmb < 0.)
- AliWarning(" stopped at not a minimum !");
- break;
- }
-
- Double_t dd=dm;
- for (Int_t div=1 ; ; div*=2) {
- Evaluate(p1,t1+dt1,r1,g1,gg1);
- Evaluate(p2,t2+dt2,r2,g2,gg2);
- dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
- dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
- if (dd<dm) break;
- dt1*=0.5; dt2*=0.5;
- if (div>512) {
- AliWarning(" overshoot !"); break;
- }
- }
- dm=dd;
-
- t1+=dt1;
- t2+=dt2;
-
- }
-
- if (max<=0) AliWarning(" too many iterations !");
-
- Double_t cs=TMath::Cos(GetAlpha());
- Double_t sn=TMath::Sin(GetAlpha());
- xthis=r1[0]*cs + r1[1]*sn;
-
- cs=TMath::Cos(p->GetAlpha());
- sn=TMath::Sin(p->GetAlpha());
- xp=r2[0]*cs + r2[1]*sn;
-
- return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
-}
-
-Double_t
-AliKalmanTrack::PropagateToDCA(AliKalmanTrack *p, Double_t d, Double_t x0) {
- //--------------------------------------------------------------
- // Propagates this track and the argument track to the position of the
- // distance of closest approach.
- // Returns the (weighed !) distance of closest approach.
- //--------------------------------------------------------------
- Double_t xthis,xp;
- Double_t dca=GetDCA(p,xthis,xp);
-
- if (!PropagateTo(xthis,d,x0)) {
- //AliWarning(" propagation failed !");
- return 1e+33;
- }
-
- if (!p->PropagateTo(xp,d,x0)) {
- //AliWarning(" propagation failed !";
- return 1e+33;
- }
-
- return dca;
-}
-
-
-
-
-
-Double_t AliKalmanTrack::MeanMaterialBudget(Double_t *start, Double_t *end, Double_t *mparam)
-{
- //
- // calculate mean material budget and material properties beween point start and end
- // mparam - returns parameters used for dEdx and multiple scatering
- //
- // mparam[0] - density mean
- // mparam[1] - rad length
- // mparam[2] - A mean
- // mparam[3] - Z mean
- // mparam[4] - length
- // mparam[5] - Z/A mean
- // mparam[6] - number of boundary crosses
- //
- mparam[0]=0; mparam[1]=1; mparam[2] =0; mparam[3] =0, mparam[4]=0, mparam[5]=0; mparam[6]=0;
- //
- Double_t bparam[6], lparam[6]; // bparam - total param - lparam - local parameters
- for (Int_t i=0;i<6;i++) bparam[i]=0; //
-
- if (!gGeoManager) {
- printf("ERROR: no TGeo\n");
- return 0.;
- }
- //
- Double_t length;
- Double_t dir[3];
- length = TMath::Sqrt((end[0]-start[0])*(end[0]-start[0])+
- (end[1]-start[1])*(end[1]-start[1])+
- (end[2]-start[2])*(end[2]-start[2]));
- mparam[4]=length;
- if (length<TGeoShape::Tolerance()) return 0.0;
- Double_t invlen = 1./length;
- dir[0] = (end[0]-start[0])*invlen;
- dir[1] = (end[1]-start[1])*invlen;
- dir[2] = (end[2]-start[2])*invlen;
- // Initialize start point and direction
- TGeoNode *currentnode = 0;
- TGeoNode *startnode = gGeoManager->InitTrack(start, dir);
- // printf("%s length=%f\n",gGeoManager->GetPath(),length);
- if (!startnode) {
- printf("ERROR: start point out of geometry\n");
- return 0.0;
- }
- TGeoMaterial *material = startnode->GetVolume()->GetMedium()->GetMaterial();
- lparam[0] = material->GetDensity();
- lparam[1] = material->GetRadLen();
- lparam[2] = material->GetA();
- lparam[3] = material->GetZ();
- lparam[4] = length;
- lparam[5] = lparam[3]/lparam[2];
- if (material->IsMixture()) {
- lparam[1]*=lparam[0]; // different normalization in the modeler for mixture
- TGeoMixture * mixture = (TGeoMixture*)material;
- lparam[5] =0;
- Double_t sum =0;
- for (Int_t iel=0;iel<mixture->GetNelements();iel++){
- sum += mixture->GetWmixt()[iel];
- lparam[5]+= mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
- }
- lparam[5]/=sum;
- }
- gGeoManager->FindNextBoundary(length);
- Double_t snext = gGeoManager->GetStep();
- Double_t step = 0.0;
- // If no boundary within proposed length, return current density
- if (snext>=length) {
- for (Int_t ip=0;ip<5;ip++) mparam[ip] = lparam[ip];
- return lparam[0];
- }
- // Try to cross the boundary and see what is next
- while (length>TGeoShape::Tolerance()) {
- mparam[6]+=1.;
- currentnode = gGeoManager->Step();
- step += snext+1.E-6;
- bparam[1] += snext*lparam[1];
- bparam[2] += snext*lparam[2];
- bparam[3] += snext*lparam[3];
- bparam[5] += snext*lparam[5];
- bparam[0] += snext*lparam[0];
-
- if (snext>=length) break;
- if (!currentnode) break;
- // printf("%s snext=%f density=%f bparam[0]=%f\n", gGeoManager->GetPath(),snext,density,bparam[0]);
- if (!gGeoManager->IsEntering()) {
- gGeoManager->SetStep(1.E-3);
- currentnode = gGeoManager->Step();
- if (!gGeoManager->IsEntering() || !currentnode) {
- // printf("ERROR: cannot cross boundary\n");
- mparam[0] = bparam[0]/step;
- mparam[1] = bparam[1]/step;
- mparam[2] = bparam[2]/step;
- mparam[3] = bparam[3]/step;
- mparam[5] = bparam[5]/step;
- mparam[4] = step;
- mparam[0] = 0.; // if crash of navigation take mean density 0
- mparam[1] = 1000000; // and infinite rad length
- return bparam[0]/step;
- }
- step += 1.E-3;
- snext += 1.E-3;
- bparam[0] += lparam[0]*1.E-3;
- bparam[1] += lparam[1]*1.E-3;
- bparam[2] += lparam[2]*1.E-3;
- bparam[3] += lparam[3]*1.E-3;
- bparam[5] += lparam[5]*1.E-3;
- }
- length -= snext;
- material = currentnode->GetVolume()->GetMedium()->GetMaterial();
- lparam[0] = material->GetDensity();
- lparam[1] = material->GetRadLen();
- lparam[2] = material->GetA();
- lparam[3] = material->GetZ();
- lparam[5] = lparam[3]/lparam[2];
- if (material->IsMixture()) {
- lparam[1]*=lparam[0];
- TGeoMixture * mixture = (TGeoMixture*)material;
- lparam[5]=0;
- Double_t sum =0;
- for (Int_t iel=0;iel<mixture->GetNelements();iel++){
- sum+= mixture->GetWmixt()[iel];
- lparam[5]+= mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
- }
- lparam[5]/=sum;
- }
- gGeoManager->FindNextBoundary(length);
- snext = gGeoManager->GetStep();
- }
- mparam[0] = bparam[0]/step;
- mparam[1] = bparam[1]/step;
- mparam[2] = bparam[2]/step;
- mparam[3] = bparam[3]/step;
- mparam[5] = bparam[5]/step;
- return bparam[0]/step;
-
-}
-
-Double_t AliKalmanTrack::GetConvConst() {
- return 1000/0.299792458/AliTracker::GetBz();
-}
-
-void AliKalmanTrack::SaveLocalConvConst() {
- //---------------------------------------------------------------------
- // Saves local conversion constant "curvature (1/cm) -> pt (GeV/c)"
- //---------------------------------------------------------------------
- if (AliTracker::UniformField()) {
- fLocalConvConst=1000/0.299792458/AliTracker::GetBz();
- } else {
- Float_t r[3]; GetXYZ(r);
- fLocalConvConst=1000/0.299792458/AliTracker::GetBz(r);
- }
-}
-